**Core Concept**
The Brachial plexus is a complex network of nerves originating from the spinal cord (C5-T1) that supply the arm, forearm, and hand. Injuries to this plexus can result in weakness or paralysis of various muscles, depending on the specific nerves affected.

**Why the Correct Answer is Right**
The patient's symptoms of weakness in the extensors of the entire arm, forearm, hand, as well as shoulder flexion and extension, are indicative of a high cervical injury involving multiple nerve roots. The involvement of C5 to T1 nerve roots would affect the musculocutaneous nerve (C5-C7), radial nerve (C5-T1), and axillary nerve (C5-C6), leading to weakness in the extensors of the arm, forearm, and hand, as well as shoulder abduction and external rotation.

**Why Each Wrong Option is Incorrect**
**Option A:** The middle and lower cord (C7-T1) would primarily affect the ulnar nerve and radial nerve, leading to weakness in the forearm and hand, but not the entire arm and shoulder.

**Option B:** The C5,6,7 roots would primarily affect the musculocutaneous nerve and radial nerve, leading to weakness in the arm and forearm, but not the entire arm, forearm, and hand.

**Option D:** The posterior trunk (C5-C6) would primarily affect the axillary nerve and radial nerve, leading to weakness in shoulder abduction and external rotation, but not the entire arm, forearm, and hand.

**Clinical Pearl / High-Yield Fact**
In Brachial plexus injuries, the key to determining the level of injury is to identify the muscles affected. The presence of weakness in the extensors of the entire arm, forearm, and hand, as well as shoulder flexion and extension, is highly suggestive of a high cervical injury involving C5 to T1 nerve roots.

**✓ Correct Answer: C. C5 to T1**